linear equation

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope (m) represent in a linear equation?

Back

The slope (m) represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

Front

What is the y-intercept (b) in a linear equation?

Back

The y-intercept (b) is the point where the line crosses the y-axis. It represents the value of y when x is 0.

Front

How do you find the y-intercept from a graph?

Back

To find the y-intercept from a graph, look for the point where the line intersects the y-axis. The coordinates of this point will be in the form (0, b).

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

How can you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope (m) but different y-intercepts (b).

Front

What does it mean if a linear equation has no solution?

Back

A linear equation has no solution if the lines are parallel, meaning they never intersect.

Front

What does it mean if a linear equation has infinitely many solutions?

Back

A linear equation has infinitely many solutions if the two lines are the same line, meaning they overlap completely.

Front

How do you convert a linear equation from standard form to slope-intercept form?

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y.

Front

What is the significance of the point (0, b) in a linear equation?

Back

The point (0, b) is the y-intercept of the line, indicating where the line crosses the y-axis.